lines_intersection support 3D

README.md

@@ -77,7 +77,6 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
 - [bijection_offset](https://openhome.cc/eGossip/OpenSCAD/lib3x-bijection_offset.html)
 - [contours](https://openhome.cc/eGossip/OpenSCAD/lib3x-contours.html)
 - [in_shape](https://openhome.cc/eGossip/OpenSCAD/lib3x-in_shape.html)	
-- [lines_intersection](https://openhome.cc/eGossip/OpenSCAD/lib3x-lines_intersection.html)	
 - [trim_shape](https://openhome.cc/eGossip/OpenSCAD/lib3x-trim_shape.html)
 
 ### 2D/3D Function
@@ -86,6 +85,7 @@ These examples incubate dotSCAD and dotSCAD refactors these examples. See [examp
 - [bezier_smooth](https://openhome.cc/eGossip/OpenSCAD/lib3x-bezier_smooth.html)	
 - [cross_sections](https://openhome.cc/eGossip/OpenSCAD/lib3x-cross_sections.html)
 - [in_polyline](https://openhome.cc/eGossip/OpenSCAD/lib3x-in_polyline.html)
+- [lines_intersection](https://openhome.cc/eGossip/OpenSCAD/lib3x-lines_intersection.html)
 - [paths2sections](https://openhome.cc/eGossip/OpenSCAD/lib3x-paths2sections.html)
 - [path_scaling_sections](https://openhome.cc/eGossip/OpenSCAD/lib3x-path_scaling_sections.html)
 - [midpt_smooth](https://openhome.cc/eGossip/OpenSCAD/lib3x-midpt_smooth.html)

docs/lib3x-lines_intersection.md

@@ -6,8 +6,8 @@ Find the intersection of two line segments. Return `[]` if lines don't intersect
 
 ## Parameters
 
-- `line1` : Two points of 2D line1.
+- `line1` : Two points of 2D or 3D line1.
-- `line2` : Two points of 2D line2.
+- `line2` : Two points of 2D or 3D line2.
 - `ext` : Default to `false`, which doesn't extend a line to an intersection with another line. 
 - `epsilon` : An upper bound on the relative error due to rounding in floating point arithmetic. Default to 0.0001.
 
@@ -21,3 +21,7 @@ Find the intersection of two line segments. Return `[]` if lines don't intersect
 
     assert(lines_intersection(line1, line2) == [0, 2.5]);
     assert(lines_intersection(line1, line3, ext = true) == [0, 10]);
+
+    line4 = [[0, 0, 0], [10, 10, 10]];
+    line5 = [[10, 0, 0], [0, 10, 10]];
+    assert(lines_intersection(line4, line5) == [5, 5, 5]);

src/__comm__/__line_intersection.scad

@@ -1,4 +1,4 @@
-function __line_intersection(line_pts1, line_pts2, epsilon = 0.0001) = 
+function __line_intersection2(line_pts1, line_pts2, epsilon = 0.0001) = 
     let(
         a1 = line_pts1[0],
         a2 = line_pts1[1],
@@ -11,3 +11,20 @@ function __line_intersection(line_pts1, line_pts2, epsilon = 0.0001) =
     )
     abs(c) < epsilon ? [] :  // they are parallel or conincident edges
         a1 + a * cross(s, b) / c;
+
+function __line_intersection3(line_pts1, line_pts2, epsilon = 0.0001) = 
+    let(
+        a1 = line_pts1[0],
+        a2 = line_pts1[1],
+        b1 = line_pts2[0],
+        b2 = line_pts2[1],
+        a = a2 - a1, 
+        b = b2 - b1, 
+        s = b1 - a1,
+        n1 = cross(a, b),
+        norm_n1 = norm(n1)
+    )
+    cross(a, s) * (b2 - a1) != 0 ||   // they aren't coplanar
+    norm_n1 < epsilon ? [] :          // they are parallel or conincident edges
+        let(n2 = cross(s, b))
+        a1 + a * (norm(n2) / norm_n1 * (n1 * n2 >= 0 ? 1 : -1));

src/_impl/_bijection_offset_impl.scad

@@ -38,7 +38,7 @@ function _bijection_offset_impl(pts, d, epsilon) =
         offset_es = _bijection__bijection_offset_edges(es, d),
         leng = len(offset_es),
         leng_minus_one = leng - 1,
-        last_p = __line_intersection(offset_es[leng_minus_one], offset_es[0], epsilon)
+        last_p = __line_intersection2(offset_es[leng_minus_one], offset_es[0], epsilon)
     )
     concat(
         last_p != [] && last_p == last_p ? [last_p] : [],
@@ -47,7 +47,7 @@ function _bijection_offset_impl(pts, d, epsilon) =
             let(
                 this_edge = offset_es[i],
                 next_edge = offset_es[i + 1],
-                p = __line_intersection(this_edge, next_edge, epsilon)
+                p = __line_intersection2(this_edge, next_edge, epsilon)
             )
             // p == p to avoid [nan, nan], because [nan, nan] != [nan, nan]
             if(p != [] && p == p) p

src/_impl/_trim_shape_impl.scad

@@ -4,7 +4,7 @@ use <../__comm__/__lines_from.scad>;
 
 function _trim_shape_any_intersection_sub(lines, line, lines_leng, i, epsilon) =
     let(
-        p = __line_intersection(lines[i], line, epsilon)
+        p = __line_intersection2(lines[i], line, epsilon)
     )
     (p != [] && __in_line(line, p, epsilon) && __in_line(lines[i], p, epsilon)) ? [i, p] : _trim_shape_any_intersection(lines, line, lines_leng, i + 1, epsilon);
 

src/lines_intersection.scad

@@ -12,8 +12,7 @@ use <__comm__/__line_intersection.scad>;
 use <__comm__/__in_line.scad>;
 
 function lines_intersection(line1, line2, ext = false, epsilon = 0.0001) =
-     let(
+     let(pt = len(line1[0]) == 2 ? __line_intersection2(line1, line2, epsilon) : 
-         pt = __line_intersection(line1, line2, epsilon)
+                                   __line_intersection3(line1, line2, epsilon))
-     )
      ext ? pt :
      pt != [] && __in_line(line1, pt, epsilon) && __in_line(line2, pt, epsilon) ? pt : [];